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Explore the mathematical concepts of singularities and Hilbert functions in this 36-minute lecture presented by M. VARBARO from the University of Genoa, Italy. Delve into the intricate relationship between these two fundamental topics in algebraic geometry and commutative algebra. Gain insights into how Hilbert functions can be used to analyze and characterize singularities, and discover their applications in various mathematical contexts. Enhance your understanding of these advanced mathematical concepts through clear explanations and examples provided by an expert in the field.